The quark masses \(m_{\lbrace u,d\rbrace ,s}\)  in this work, in general, are different from those in LFH with IMA. As mentioned above, our quark masses satisfy the GMOR relation (REF ), \(M^2_{\pi } = 2\sigma m_{u,d} + 4 m_{u,d}^2\) , \(M^2_K= \sigma (m_{u,d}+m_s) + (m_{u,d}+m_s)^2\) .
Another constraint comes from the mass splitting between the vector meson (\(1^{--}\) ) and the axial-vector meson (\(1^{+-}\) ), which is sensitive to \(\sigma \) : \(M^2_{b_1} - M^2_{\rho } = 2 \sigma ^2 + 4 \sigma m_{u,d}\) , \(M^2_{K_1(1400)} - M^2_{K^*(892)} = 2 \sigma ^2 + 2 \sigma (m_{u,d} + m_s)\) .
The resulting quark masses \(m_{u,d} = 15\,\mathrm {MeV}\) , \(m_s = 261\,\mathrm {MeV}\)  are slightly larger than the current quark mass, yet lower than those from LFH with IMA (\(m_{u,d}=46 \,\mathrm {MeV}\) , \(m_s = 357\,\mathrm {MeV}\) ), and far lower than the typical constituent quark masses (\(m_{u,d} \sim 350\,\mathrm {MeV}\) ).
Note that the quark masses in this work are effective quark masses at low energy resolution [1]}, which are in general different from the current quark masses appearing in, e.g., Lattice QCD [2]}.
Note that \(\sigma \)  obtained from the \(q\bar{q}\)  mesons and the \(s\bar{q}\)  mesons coincide, which is consistent with the Weinberg relation [3]}, [4]}.
The condensate is predicted to be \(\langle \bar{q} q \rangle = f_\pi ^2\sigma = (0.26\,\mathrm {GeV})^3\) . This is compared with the standard value from chiral perturbation theory \(\langle \bar{q} q \rangle _{\overline{\mathrm {MS}}}^{\mu =2\,\mathrm {GeV}} = (0.34\,\mathrm {GeV})^3\) .
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